Question: Rewrite as a simplified fraction. ${0.\overline{29} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 29.2929...\\ 1x &= 0.2929...\end{align*}}$ Subtracting the two equations, we have: ${99x = 29}$ ${x = \dfrac{29}{99}} $